Comparison between Euler, Heun, Runge-Kutta and Adams-Bashforth-Moulton integration methods in the particle dynamic simulation

At this time, research topic about the nano scale particle dynamics simulation is an emerging research today. Some particle simulation using Euler integration method, but Euler method is the simplest integration method and used only for the smooth particle moving. For extreme abrupt motion of particle, it is necessary to study other integration methods. This paper discusses the computing comparison of Euler, Heun, fourth order Runge-Kutta and third order Adams-Bashforth-Moulton integration used in particle dynamics simulation. The program written in C++ programming languages using Microsoft Visual Studio 2010 compiler and run on Intel i7 processor. The results of computational simulations show that the Euler integration method is the fastest integration with average computation time at 0.055592 second. Whereas the slowest integration is Adams - Bashforth - Moulton with average computation time at 0.055869 second. Simulations also shows that Euler integration method is suitable for smooth motion of particle, whereas Adam-Bashforth-Moulton integration method is suitable for extreme abrupt motion of particle.